I can only answer your battery questions.
No, you do not need the battery door. However the battery does have to be pushed up pretty tight to mate properly with the contacts.
Looking at my PZ-20 it looks like you'll have to remove teh bottom plate. I don't know how hard the job will be.
Too bad that they don't have any power grips, that I'm aware of for the PZ line. They would eliminate the problem, and make new batteries both more affordable and easier to buy.
Pentax did make a handful of power zooms. I believe that they're all part of the FA lens lineup. I've never tried any, or done any research on them. We have one at the lab, where I work... however it seems to be jammed so I have no intention of trying it and possibly damaging my camera